After the main cold symptoms fade, a dry or tickly cough often remains because the lining of the airways stays irritated and sensitive for a while. This is sometimes called a post-viral or post-infectious cough and it does not mean the infection is still active.
For most people it improves steadily over two to three weeks. In a minority it can drag on for six to eight weeks, especially after a chest infection or in people who are sensitive to airway irritants.
If the cough is not slowly improving, is getting worse, brings up discoloured phlegm with fever, or comes with wheezing or breathlessness, see a doctor. A cough lasting beyond 8 weeks should always be assessed.